Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.3/62786

Title

Numerical method for evolving the dipolar projected Gross-Pitaevskii equation

Author(s)

Blakie, P. B.;  Ticknor, C.;  Bradley, A. S.;  Martin, A. M.;  Davis, M. J.;  Kawaguchi, Y.

Abstract

We describe a method for evolving the projected Gross-Pitaevskii equation (PGPE) for an interacting Bose gas in a harmonic-oscillator potential, with the inclusion of a long-range dipolar interaction. The central difficulty in solving this equation is the requirement that the field is restricted to a small set of prescribed modes that constitute the low-energy c-field region of the system. We present a scheme, using a Hermite-polynomial-based spectral representation, which precisely implements this mode restriction and allows an efficient and accurate solution of the dipolar PGPE. We introduce a set of auxiliary oscillator states to perform a Fourier transform necessary to evaluate the dipolar interaction in reciprocal space. We extensively characterize the accuracy of our approach and derive Ehrenfest equations for the evolution of the angular momentum.

Publication type

Journal article

Research centre

Swinburne University of Technology. Faculty of Engineering and Industrial Sciences. Centre for Atom Optics and Ultrafast Spectroscopy. ARC Centre of Excellence for Quantum-Atom Optics

Source

Physical Review E, Vol. 80, no. 1 (Jul 2009)

Publication year

2009

FOR Code(s)

0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics;  0203 Classical Physics

Keyword(s)

Bose gases;  Dipolar interactions;  Einstein condensation dynamics;  Gross-Pitaevskii equation

Publisher

American Physical Society

ISSN

1539-3755

Publisher URL

http://dx.doi.org/10.1103/PhysRevE.80.016703

Copyright

Copyright © 2009 The American Physical Society.

Peer reviewed